Talk:Geodesic convexity

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[edit] Relation to convex metric space

I realize that Riemannian metrics are not the same thing as distance metrics, but the definition of convexity here is almost the same as that in convex metric space (or rather, not the main definition there, but the related one mentioned in the article and used more explicitly e.g. in injective metric space that any pair of points can be connected by the isometric image of a line segment). Should there be a closer connection between these articles? Merge, maybe? Or rename this article geodesic metric space, discuss in it non-Riemannian as well as Riemannian metrics, clarify the difference between that and the notion of convexity discussed in convex metric space, and link articles that need this version of the concept, such as injective metric space, to here instead of there? —David Eppstein 17:09, 8 August 2007 (UTC)